It may seem strange that Adam and Eve's sin was punished so severely that human nature itself was changed, yet on reflection this makes sense, given how easy it would have been for them to obey.
In fact, the external act of eating the fruit, tiny sin though it was, really reflected an internal sin that had already occurred. They had already committed the sin of pride in their hearts when their bodies took and ate of the fruit. "Our first parents, then, must already have fallen before they could do the evil deed, before they could commit the sin of eating the forbidden fruit."
This internal sin was the result of cutting themselves (and hence, all humans) off from God. When it seemed that they were being elevated by striving to be God, in reality they were being cast down--just as when we humble ourselves before the Lord we are raised up. "The reason for this is that holy lowliness makes us bow to what is above us and, since there is nothing above God, the kind of lowliness that makes us close to God exalts us."
Thus, humility is the key virtue of the City of God here on earth, while pride is the vice most associated with the city of man. "The one City began with the love of God; the other had its beginnings in the love of self."
Fortunately, God provides an "out." When we recognize our own sin (the Puritans would call this "conviction") and reject it, we have the chance to embrace the offer of salvation through the Gospel in faith.
Pride, however, resists this conviction because it tries to deny that there is a sin to be forgiven, or at the very least it tries to blame someone else for the sin (as Adam did Eve, and Eve did the serpent). Yet this in no way lessens our guilt before a Holy God.